Finite Group Databasebeta

← Group #309482

Character table — Group #309482

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111111112222222244444444444444444488888888888888888888888816161616161616161616161632
order12222222444444444444444444888888882244444488888888888888882244444488884
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111-1-11-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-11111-11-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111111
χ5111111111111111111111-1-1-1-111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-11-1-1-111-1-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111
χ7111111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111-111111-1-1-1
χ911111111111111111-1-1-1-11111111111111-1-11111-1-111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-111-1-1-1-111-1-111111111-1-1-1-1-1-111-1-1-1-111-1-11
χ1111111111111111111-1-1-1-111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-111-1-111-1
χ1311111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11
χ1411111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111-1-1-11111111-1
χ1511111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-11111-1
χ1611111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-111111111111111-1-111-1-1-1-1-1-11
χ172222222222-2-222-2-2-222220000-222220000220000-2-2-2-2000000000000000000-200000000
χ182222222222-2-222-2-2-222220000-2-2-2-2-20000-2-20000-2-222000000000000000000200000000
χ192222222222-2-222-2-2-2-2-2-2-20000-222220000-2-2000022-2-2000000000000000000200000000
χ202222222222-2-222-2-2-2-2-2-2-20000-2-2-2-2-200002200002222000000000000000000-200000000
χ2122222222-2-222-2-222-200002222-20000222200-2-2220000-2-200000000000000000-20000000
χ2222222222-2-222-2-222-200002222-20000-2-2-2-200-2-2-2-20000220000000000000000020000000
χ2322222222-2-222-2-222-20000-2-2-2-2-2000022220022-2-20000-2-20000000000000000020000000
χ2422222222-2-222-2-222-20000-2-2-2-2-20000-2-2-2-200222200002200000000000000000-20000000
χ25222-2-2-2-222-2002-200022-2-20000022-2-2i2i2−i2−i22-200000000i2−i20000i2i2−i2−i2i2i2−i2−i200000000i2−i2000
χ26222-2-2-2-222-2002-200022-2-20000022-2-2−i2−i2i2i22-200000000−i2i20000−i2−i2i2i2−i2−i2i2i200000000−i2i2000
χ27222-2-2-2-222-2002-200022-2-200000-2-222i2i2−i2−i2-2200000000i2−i20000i2i2−i2−i2−i2−i2i2i200000000−i2i2000
χ28222-2-2-2-222-2002-200022-2-200000-2-222−i2−i2i2i2-2200000000−i2i20000−i2−i2i2i2i2i2−i2−i200000000i2−i2000
χ29222-2-2-2-222-2002-2000-2-2220000022-2-2i2i2−i2−i2-2200000000i2−i20000−i2−i2i2i2i2i2−i2−i200000000−i2i2000
χ30222-2-2-2-222-2002-2000-2-2220000022-2-2−i2−i2i2i2-2200000000−i2i20000i2i2−i2−i2−i2−i2i2i200000000i2−i2000
χ31222-2-2-2-222-2002-2000-2-22200000-2-222i2i2−i2−i22-200000000i2−i20000−i2−i2i2i2−i2−i2i2i200000000i2−i2000
χ32222-2-2-2-222-2002-2000-2-22200000-2-222−i2−i2i2i22-200000000−i2i20000i2i2−i2−i2i2i2−i2−i200000000−i2i2000
χ3322-22-22-2-222-2-2-2-222-200002i2i−2i−2i200000000002i−2i0000000000002-22-20000002i−2i000000000
χ3422-22-22-2-222-2-2-2-222-200002i2i−2i−2i200000000002i−2i000000000000-22-22000000−2i2i000000000
χ3522-22-22-2-222-2-2-2-222-20000−2i−2i2i2i20000000000−2i2i0000000000002-22-2000000−2i2i000000000
χ3622-22-22-2-222-2-2-2-222-20000−2i−2i2i2i20000000000−2i2i000000000000-22-220000002i−2i000000000
χ3722-22-22-2-2-2-22222-2-2-22i−2i2i−2i00002000000000000002i−2i000022-2-2000000000000002i−2i00000
χ3822-22-22-2-2-2-22222-2-2-22i−2i2i−2i00002000000000000002i−2i0000-2-22200000000000000−2i2i00000
χ3922-22-22-2-2-2-22222-2-2-2−2i2i−2i2i0000200000000000000−2i2i000022-2-200000000000000−2i2i00000
χ4022-22-22-2-2-2-22222-2-2-2−2i2i−2i2i0000200000000000000−2i2i0000-2-222000000000000002i−2i00000
χ4122-22-22-2-2-2-2-2-2222222i−2i2i−2i2i2i−2i−2i-20000000000−2i2i00−2i2i00000000000000002-200000000000
χ4222-22-22-2-2-2-2-2-2222222i−2i2i−2i−2i−2i2i2i-200000000002i−2i00−2i2i0000000000000000-2200000000000
χ4322-22-22-2-2-2-2-2-222222−2i2i−2i2i2i2i−2i−2i-20000000000−2i2i002i−2i0000000000000000-2200000000000
χ4422-22-22-2-2-2-2-2-222222−2i2i−2i2i−2i−2i2i2i-200000000002i−2i002i−2i00000000000000002-200000000000
χ452-22-222-2-2002-2002-2000002i−2i2i−2i0i2−i2i2−i22-22-200002i−2i00i2−i2002−22−20000i2−i2i2−i200000000002−20
χ462-22-222-2-2002-2002-2000002i−2i2i−2i0i2−i2i2−i2-22-220000−2i2i00i2−i2002−22−20000−i2i2−i2i20000000000−220
χ472-22-222-2-2002-2002-2000002i−2i2i−2i0−i2i2−i2i22-22-200002i−2i00−i2i200−22−220000−i2i2−i2i20000000000−220
χ482-22-222-2-2002-2002-2000002i−2i2i−2i0−i2i2−i2i2-22-220000−2i2i00−i2i200−22−220000i2−i2i2−i200000000002−20
χ492-22-222-2-2002-2002-200000−2i2i−2i2i0i2−i2i2−i22-22-20000−2i2i00i2−i200−22−220000i2−i2i2−i20000000000−220
χ502-22-222-2-2002-2002-200000−2i2i−2i2i0i2−i2i2−i2-22-2200002i−2i00i2−i200−22−220000−i2i2−i2i200000000002−20
χ512-22-222-2-2002-2002-200000−2i2i−2i2i0−i2i2−i2i22-22-20000−2i2i00−i2i2002−22−20000−i2i2−i2i200000000002−20
χ522-22-222-2-2002-2002-200000−2i2i−2i2i0−i2i2−i2i2-22-2200002i−2i00−i2i2002−22−20000i2−i2i2−i20000000000−220
χ5344444444-4-4-4-4-4-4-4-44000000004000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4400-4400000000000000002i22i2−2i2−2i20000000000−2i22i20000000000000000000000000
χ55444-4-4-4-44-4400-440000000000000000−2i2−2i22i22i200000000002i2−2i20000000000000000000000000
χ5644-44-44-4-44444-4-4-4-4400000000-4000000000000000000000000000000000000000000000
χ5744-4-44-44-44-400-440000000000000000000000000000000000002i2−2i2−2i22i200000000000000000
χ5844-4-44-44-44-400-44000000000000000000000000000000000000−2i22i22i2−2i200000000000000000
χ5944-4-44-44-4-44004-40004i−4i−4i4i00000000000000000000000000000000000000000000000000
χ6044-4-44-44-4-44004-4000−4i4i4i−4i00000000000000000000000000000000000000000000000000
χ614-444-4-44-40000000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000-222-20000000000000
χ624-444-4-44-40000000000000000002i2−2i2−2i22i2−2i22i22i2−2i2000000000000000000002-2-220000000000000
χ634-444-4-44-4000000000000000000−2i22i22i2−2i22i2−2i2−2i22i2000000000000000000002-2-220000000000000
χ644-444-4-44-4000000000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000-222-20000000000000
χ654-44-444-4-400-4400-4400000000002i2−2i22i2−2i2000000000000−2i22i2000000000000000000000000000
χ664-44-444-4-400-4400-440000000000−2i22i2−2i22i20000000000002i2−2i2000000000000000000000000000
χ674-4-4-4-4444004-400-4400000000000000000000000000000022−22−2222000000000000000000000
χ684-4-4-4-4444004-400-44000000000000000000000000000000−222222−22000000000000000000000
χ694-4-4-4-444400-44004-4000004-4-440000000000000000000000000000000000000000000000
χ704-4-4-4-444400-44004-400000-444-40000000000000000000000000000000000000000000000
χ718-8-888-8-88000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).